The requirements for any aircraft to operate in Cat 2/3 conditions are given in the appropriate regulations; JAR-AWO, or AC120-29, etc. These specify the necessary onboard equipment and reliability, the latter may include the aircraft systems – dual electrical systems etc. Thus, any suitably equipped aircraft can fly in low vis conditions, the type and extent of equipment determines the lowest minima that may be used.
In Europe, there were differences between commercial operations and ‘bizjet’ aircraft, although these were generally in operational approval. The operational requirements for Cat 2/3 are now standardised in JAR-OPS1 and the revised AC120-29 series.
In Europe a commercial operator has to gain approval from his authority before commencing operations; I think that this includes a list of airfields/runways to be used for Cat 2/3 operations and an agreement from the airport / country involved; thus ATC should be aware of the operator's capability / approval.